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a) A=x^3 + 3x^2*5 + 3x*5^2 + 5^3
=(x+5)^3
Thay x = -10 vào biểu thức A ta được:
A = (-10+5)^3
=(-5)^3
=-75
Làm tương tự nhé
Bài 3 Tính nhanh
A, 892^2+892.216+108^2 B, 36^2+26^2-52.36
=892^2+2.892.108+108^2 =36^2-52.62+26^2
=(892+108)^2
=1000^2
=1000000
Bài 4 Phân tích đa thức sau thành nhân tử
X^3-2x^2+x
5(x-y)-y(x-y)
36-12x+x^2
4x^2+12x-9
Bài 3:
\(892^2+892.216+108^2=892^2+2.892.108+108^2=\left(892+108\right)^2=1000000\)
\(36^2+26^2-52.36=36^2-2.26.36+26^2=\left(36-26\right)^2=100\)
Bài 4:
\(x^3-2x^2+x=x.\left(x^2-2x+1\right)=x.\left(x-1\right)^2\)
\(5.\left(x-y\right)-y.\left(x-y\right)=\left(5-y\right)\left(x-y\right)\)
\(36-12x+x^2=x^2-12x+36=x^2-2x.6+6^2=\left(x-6\right)^2\)
\(4x^2+12x-9=\left(2x\right)^2+2.2x.3+3^2=\left(2x+3\right)^2\)
\(x^2-5y+y^2-2xy+5x=\left(x^2-2xy+y^2\right)+\left(5x-5y\right)\)
a/ x2 – 5y + y2 -2xy + 5x = ( x2 - 2xy + y2 ) - 5( y - x ) = ( x - y )2 - 5( y - x ) = ( y - x )2 - 5( y - x ) = ( y - x )( y - x - 5 )
b/ 4x2 – 81(y – 2)2 = 4x2 - 92(y – 2)2= 4x2 – ( 9y – 18)2 = ( 2x -9y -18 )( 2x + 9y + 18 )
c/ x2z – y2z + 2yz – z = ( x2z + yz ) - ( y2z - yz ) - z = z( x2 + y ) - z( y2 - y ) -z = z( x2 + y - y2 +y - 1 ) = z( x2 + 2y - y2 - 1 ) \(=z[x^2-\left(y^2-2y+1\right)]=z[x^2-\left(y-1\right)^2=z\left(x-y+1\right)\left(x+y-1\right)\)
d/ x3 – 8y3 + x2 + 2xy + 4y2 = ( x3 – 8y3 ) + x2 + 2xy + 4y2 = ( x -2y )( x2 + 2xy + 4y2 ) + ( x2 + 2xy + 4y2 0 = ( x2 + 2xy + 4y2)( x -2y +1)
e/ 7x2 – 11x + 4 = 7x2 -7x -4x +4 = 7x( x-1 ) - 4( x - 1 ) = ( x - 1 )( 7x - 4 )
g/ 13x2 + 2xy – 15y2 = 13x2 - 13xy + 15xy - 15y2 = 13x( x - y ) + 15y( x - y ) = ( x - y )( 13x + 15y )
h/ x3 + 3x2 + 3x + 2 = x3 +2x2 + x2 +2x + x + 2 = x2( x + 2 ) + x( x + 2 ) + ( x + 2 ) = ( x + 2 )( x2 + x + 1 )
i/ x3 – 3x2 + 3x – 2 + xy – 2y = x3 - 2x2 - x2 + 2x + x - 2 +xy - 2y = x2( x - 2 ) - x( x - 2 ) + ( x - 2 ) + y( x - 2 ) = ( x - 2 )( x2 - x +1 + y )
a, \(\left(x+y\right)^2+\left(x-y\right)^2=x^2+2xy+y^2+x^2-2xy+y^2=2x^2+2y^2\)
b, \(\left(x-y\right)^2+2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2=\left(x-y+x+y\right)^2=4x^2\)
a) \(\left(x+y\right)^2+\left(x-y\right)^2\)
\(=x^2+2xy+y^2+x^2-2xy+y^2=2x^2+2y^2\)
b) \(2\left(x-y\right)\left(x+y\right)+\left(x-y\right)^2+\left(x+y\right)^2\)
\(=\left(x-y\right)^2+2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2\)
\(=\left[\left(x-y\right)^2+\left(x+y\right)^2\right]\)
\(=\left(x-y+x+y\right)^2=\left(2x\right)^2=4x^2\)
a, (\(x\) + y).(\(x\) + y)2 - 3\(xy\).(\(x\) + y)
= (\(x+y\))3 - 3\(x^2\)y - 3\(xy^2\)
= \(x^3\) + 3\(x^2\).y + 3\(xy^2\) + y3 - 3\(x^2\).y - 3\(xy^2\)
= \(x^3\) + y3
b, (\(x-y\)).(\(x-y\))2 - 3\(xy\).(\(x-y\))
= (\(x\) - y)3 - 3\(x^2\).y + 3\(xy^2\)
= \(x^3\) - 3\(x^2\)y + 3\(xy^2\) - y3 - 3\(x^2\)y + 3\(xy^2\)
= \(x^3\) - 6\(x^2\)y + 6\(xy^2\) - y3